
holds. In view of the existential quantifier in the above formula, a natural categorical context in which to extend this condition is the context of regular categories in the sense of [1]}. In addition to the examples of matrix properties mentioned above, one has now also the example of \(n\) -permutable categories [2]}. The exactness properties on a regular category being expressible by finite conjunctions of such matrix conditions have been semantically characterized in [3]}.
